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DBSCAN results

Hi,as far as I understood DBSCAN, there should be core points, border points and noise.I wonder how to identify the borderpoints in the results tab.? I refer to the explanation found here: http://www-users.cs.umn.edu/~kumar/dmbook/ch8.pdfAny help on that?

Maybe I am wrong but it seems to me that not in all cases the Cluster_0 is filled with noise. I just quick checked with R [fpc package] an easy example where NO noise should occur. However the cluster_0 is existent in rapidminer. I guess its a valid cluster result rather than noise.